The power converter has failed on the Notebook, and this is probably my fault for stressing the cable by folding it to fit into a pencil case.
It sounds as if the power supply still works, but the cable is damaged internally. I usually MacGyver them: cut open the power supply, cut 10 cm off the cable, solder it, and glue/tape it back together. Note: only do this if you're comfortable doing this safely.
It is rated at 45 watts if I remember correctly. I can buy a compatible product tht is rated at 90 watts max. I'm assuming that the higher rating will allow it to run with less stress, and should prolong its life.
I doubt it matters, if a mechanical failure in a cable is what broke your current power supply.
Now for the real question. I've noticed that the windows machine is taking far longer to recharge - up to 3 times as long. It seems to disconnect the battery for much of the time, Is this an indication of a failing battery?
It could just as well charge slower by design. If the battery works, I wouldn't worry about it (yet).
Recently I've been running the notebook on battery until it is almost flat, and then recharging completely within 24 hours. Should I reduce the number of times that I discharge the battery?
What I do, is run on grid power when possible, and battery power when needed. I never try to deep cycle any batteries, it reduces your battery life.
I'm planning to dump Windows and switch to Linux, and to replace the HDD with as SSD, but as a result of some other issues I have to resolve, I've put off spending the time on this. Should I give this upgrade an increased priority to preserve the life of my notebook?
As much as I dislike Windows, I don't think it causes more wear to your hardware than Linux.